(1/x^2)-(1/x)=4

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Solution for (1/x^2)-(1/x)=4 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

1/(x^2)-(1/x) = 4 // - 4

1/(x^2)-(1/x)-4 = 0

1/(x^2)-x^-1-4 = 0

x^-2-x^-1-4 = 0

t_1 = x^-1

1*t_1^2-1*t_1^1-4 = 0

t_1^2-t_1-4 = 0

DELTA = (-1)^2-(-4*1*4)

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)+1)/(1*2) or t_1 = (1-17^(1/2))/(1*2)

t_1 = (17^(1/2)+1)/2 or t_1 = (1-17^(1/2))/2

t_1 = (1-17^(1/2))/2

x^-1-((1-17^(1/2))/2) = 0

1*x^-1 = (1-17^(1/2))/2 // : 1

x^-1 = (1-17^(1/2))/2

-1 < 0

1/(x^1) = (1-17^(1/2))/2 // * x^1

1 = ((1-17^(1/2))/2)*x^1 // : (1-17^(1/2))/2

2*(1-17^(1/2))^-1 = x^1

x = 2*(1-17^(1/2))^-1

t_1 = (17^(1/2)+1)/2

x^-1-((17^(1/2)+1)/2) = 0

1*x^-1 = (17^(1/2)+1)/2 // : 1

x^-1 = (17^(1/2)+1)/2

-1 < 0

1/(x^1) = (17^(1/2)+1)/2 // * x^1

1 = ((17^(1/2)+1)/2)*x^1 // : (17^(1/2)+1)/2

2*(17^(1/2)+1)^-1 = x^1

x = 2*(17^(1/2)+1)^-1

x in { 2*(1-17^(1/2))^-1, 2*(17^(1/2)+1)^-1 }

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